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Kinks and domain walls are the simplest kind of solitons and are invaluable for testing various ideas and for learning about non-perturbative aspects of field theories. They are the subject of research in essentially every branch of physics, ranging from condensed matter to cosmology. This book is an introduction to kinks and domain walls and their principal classical and quantum properties. The book examines classical solitons, building from examples in elementary systems to more complicated settings. The formation of solitons in phase transitions, their dynamics, and their cosmological consequences are further discussed. The book closes with an explicit description of a few laboratory systems containing solitons. Kinks and Domain Walls includes several state-of-the-art results, some previously unpublished. Each chapter closes with open questions and research problems. This book will be of great interest to both graduate students and academic researchers in theoretical physics, particle physics, cosmology and condensed matter physics.